A POTENTIAL-BASED CONSTRUCTION OF THE INCREASING SUPERMARTINGALE COUPLING

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Deng, Shuoqing; Norgilas, Dominykas
• 署名单位: University of Michigan System; University of Michigan; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1907
• 发表日期: 2023
• 页码: 3803-3834
• 关键词: explicit martingale version; Optimal Transport; bounds; DECOMPOSITION; MARGINALS; lyrebirds; peacocks; plans

摘要

The increasing supermartingale coupling, introduced by Nutz and Stebegg (Ann. Probab. 46 (2018) 3351-3398) is an extreme point of the set of supermartingale couplings between two real probability measures in convex-decreasing order. In the present paper we provide an explicit construction of a triple of functions, on the graph of which the increasing super -martingale coupling concentrates. In particular, we show that the increasing supermartingale coupling can be identified with the left-curtain martingale coupling and the antitone coupling to the left and to the right of a uniquely determined regime-switching point, respectively.Our construction is based on the concept of the shadow measure. We show how to determine the potential of the shadow measure associated to a supermartingale, extending the recent results of Beiglbock et al. (Electron. Commun. Probab. 27 (2022) 1-12) obtained in the martingale setting.